It shames me to admit it, but I feel like I still haven’t figured out the right way to efficiently read papers and textbooks. I am a second year PhD student in pure mathematics, and I struggle a lot to balance the need to learn a lot new mathematics with the fact that I have a finite amount of time in which to do it.
I should have asked this question years ago: what is best (i.e. most efficient) way to read papers and textbooks in order to have a working knowledge of the subject?
Maybe I should be more precise. I am working in both algebraic geometry and homotopy theory (think simplicial presheaves and K-Theory), and I have recently found myself overwhelmed by the amount that I need to learn. In an ideal world I would read background material by doing every exercise in every textbook, and by working carefully through every proof in every paper, but I worry that I just don’t have enough time. On the flip side, I often find myself “reading” mathematics without actually absorbing any working knowledge, so I basically don’t make any direct research progress.
I understand that reading in great volume is still constructive, and I have certainly learnt a lot about how mathematics fits together, but when I actually need to do new mathematics I consistently find myself lost.
To rephrase my question: can anyone offer an advice on their workflow when it comes to learning new mathematics?
Perhaps the way I feel is more or less how everyone feels, and it is confidence and organisation which is the problem. If that is the case, then I ask: can anyone offer advice on how to organise oneself day to day in a PhD to be productive? Moreover, can anyone offer advice on how to break out of a lack of self confidence when it comes to doing research mathematics?
I apologise in advance if this question has been asked many times before, but I haven’t been able to find the right thread. I apologise also if my questions are too multi-pronged, I just feel that they are all to interconnected to be split up.